The only guaranteed result of using premium gas in an engine designed for regular is that you will spend more money. As far as any tangible benefits, the chances are slim to none.
If your engine runs fine on regular, filling it with premium is unlikely to boost acceleration or fuel economy by more than insignificant amounts. No matter what you've heard, premium won't do more to clean deposits from your fuel injectors or other parts of the fuel system because today's regular gas contains the same detergent additives.
The main difference with premium is its higher-octane rating, 91 or higher compared with 87 for regular. The higher octane gives premium gas greater resistance to early fuel ignition, which can result in potential damage, sometimes accompanied by audible engine knocking or pinging. Higher octane allows engines to have higher compression ratios (for a more energetic explosion), more advanced ignition timing or forced-air induction like turbochargers or superchargers. They perform best when fed premium gas.
But if the vehicle manufacturer says your engine needs only 87-octane regular, that is what you should use. The higher octane of premium gas won't make your car faster. The opposite is possible, because higher-octane gasoline technically has less energy than lower-octane; it's the fuel's ability to be compressed more without pre-igniting that results in more power when used in the appropriate engine. Premium gas is not "stronger."
If you burn premium because you think it makes the engine peppier, that is probably psychological: I'm paying more, so I must be getting more. Some motorists claim they get better fuel economy with premium, but some of that could be due to favorable weather conditions (such as warm weather instead of cold) or other factors.
If you use premium because your engine knocks on regular, you are treating the symptom, not the cause. Something else might be causing the knock, such as carbon deposits or hot spots that should be diagnosed and treated by a mechanic.
Premium gas can cost 20 to 60 cents more per gallon, depending on where you live. Paying more to pump premium into a car designed for regular will have a low return on investment.